# A family of quasi-local mass functionals with monotone flows

Conference Paper

© 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. We define a one parameter family of quasi-local mass functionals m c (Σ), 0 ≤ c ≤ ∞, which are nondecreasing on surfaces in 3-manifolds with nonnegative scalar curvature with respect to a one parameter family of flows. In the case that c = 0, m 0 (Σ) equals the Hawking mass of Σ 2 and the corresponding flow is inverse mean curvature flow. Then, following the arguments of Geroch [8], Jang and Wald [12] , and Huisken and Ilmanen [9], we note that the generalization of their results for inverse mean curvature flow would imply that if m ADM is the total mass of the complete, asymptotically flat 3-manifold with nonnegative scalar curvature, then m ADM ≥ m c (Σ) for all nonnegative c and all connected surfaces Σ which are not enclosed by surfaces with less area.

### Full Text

### Duke Authors

### Cited Authors

- Bray, HL

### Published Date

- January 1, 2006

### Start / End Page

- 323 - 329

### International Standard Book Number 13 (ISBN-13)

- 9789812704016

### Digital Object Identifier (DOI)

- 10.1142/9789812704016_0030

### Citation Source

- Scopus